The 'Fujitsu' that made the shitty software was a British consulting company that was acquired by Fujitsu [1] to farm public contracts. This is made by the Japanese parent company.
You're right, but the scandal is so upsetting that I personally cannot ever look at Fujitsu the same way even. Also, I think you're neglecting that a large part of why it became so bad was that Fujitsu claimed there was no issue with their software. Even if it were built by a company they acquired, the response to the developing situation was something that the parent company should have stepped in to oversee.
In a very specific legal sense, it isn't, we are talking about two entirely separate legal entities (and ultimately groups of people) which have a relation of ownership, not directorship.
[1] https://en.wikipedia.org/wiki/International_Computers_Limite...